Relationships Between Masses of Elements and Compounds

In general, the conversions you will be doing in chemistry require you to convert amount of one substance (substance 1) to amount of another substance (substance 2). Such conversions can be done in three basic steps  

Mass is often the most easily measured property, and we now know how to convert between mass in grams and moles of a substance using the substance s molar mass. The solutions to many problems will therefore follow these steps  

To complete these steps, we need one additional kind of conversion factor that converts between moles of an element and moles of a compound containing that element. We obtain this conversion factor from the compound s chemical formula. For example, the formula for hexane, C6H14, tells us that each hexane molecule contains six 

One mole of the oxygen found in air, O2, contains 6.022 X molecules and 1.204 X 10 (two times 6.022 X 10 ) oxygen atoms. There are two moles of oxygen atoms in one mole of oxygen molecules. 

Similarly, we can use ionic formulas to generate conversion factors that convert between moles of atoms of each element in an ionic compound and moles of compound. For example, the formula for calcium nitrate, Ca(N03)2, yields the following conversion factors. 

---

Section 9.4 Relationships Between Masses of Elements and Compounds... 

In Chapter 6, we learned how a chemical formula contains conversion factors for converting between moles of a compound and moles of its constituent elements. In this chapter, we have seen how a chemical equation contains conversion factors between moles of reactants and moles of products. However, we are often interested in relationships between mass of reactants and mass of products. For example, we might want to know the mass of carbon dioxide emitted by an automobile per kilogram of gasoline used. Or we might want to know tire mass of each reactant required to obtain a certain mass of a product in a S5mthesis reaction. These calculations are similar to calculations covered in Section 6.5, where we converted between mass of a compound and mass of a constituent element. The general outline for these types of calculations is ... 

In this chapter, you will learn about the relationships between chemical formulas, molar masses, and the masses of elements in compounds. 

A chemical equation describes a chemical reaction in many ways as an empirical formula describes a chemical compound. The equation describes not only which substances react, but the relative number of moles of each undergoing reaction and the relative number of moles of each product formed. Note especially that it is the mole ratios in which the substances react, not how much is present, that the equation describes. In order to show the quantitative relationships, the equation must be balanced. That is, it must have the same number of atoms of each element used up and produced (except for special equations that describe nuclear reactions). The law of conservation of mass is thus obeyed, and also the "law of conservation of atoms. Coefficients are used before the formulas for elements and compounds to tell how many formula units of that substance are involved in the reaction. A coefficient does not imply any chemical bonding between units of the substance it is placed before. The number of atoms involved in each formula unit is multiplied by the coefficient to get the total number of atoms of each element involved. Later, when equations with individual ions are written (Chap. 9), the net charge on each side of the equation, as well as the numbers of atoms of each element, must be the same to have a balanced equation. The absence of a coefficient in a balanced equation implies a coefficient of 1. 

The elements C and H form more than one compound. The graph opposite gives the relationship between the masses of the constituents, C and H, and the masses of the both compounds formed. If the molecular formula of the first compound is CH4, what is the empirical formula of the second compound ... 

I he previous chapters showed how the laws of conservation of mass and con--1- servation of atomic identity, together with the concept of the mole, determine quantitative mass relationships in chemical reactions. That discussion assumed prior knowledge of the chemical formulas of the reactants and products in each equation. The far more open-ended questions of which compounds are found in nature (or which can be made in the laboratory) and what types of reactions they undergo now arise. Why are some elements and compounds violently reactive and others inert Why are there compounds with chemical formulas H2O and NaCl, but never H3O or NaCli Why are helium and the other noble gases monatomic, but molecules of hydrogen and chlorine diatomic All of these questions can be answered by examining the formation of chemical bonds between atoms. 

To answer this question, we need to know the chemical composition of sodium chloride. From Chapter 5, we are familiar with its formula, NaCl, so we know that there is one sodium ion to every chloride ion. However, since the masses of sodium and chlorine are different, the relationship between the mass of sodium and the mass of sodium chloride is not clear from the chemical formula alone. In this chapter, we learn how to use the information in a chemical formula, together with atomic and formula masses, to calculate the amount of a constituent element in a given amount of a compound (or vice versa). 

In Sample Problems 3.6 and 3.7, we used a compound s formula to find the mass percent (or mass fraction) of each element in it and the mass of an element in any size sample of it. In this section, we do the reverse we use the masses of elements in a compound to find the formula. Then, we look briefly at the relationship between molecular formula and molecular structure. 

The sum of the atomic masses of all the atoms in a chemical formula is called the formula mass (4.5). It is a conversion factor between mass of the compound and moles of its molecules. The numerical relationships inherent in chemical formulas can help us determine the amount of a given element within a given compound (4.6). 

Notice that atomic mass and the molar mass of carbon-12 are numerically equal. They differ only in units atomic mass is measured in atomic mass units, and molar mass is measured in grams per mole. The same relationships exist between atomic and molar masses of elements, between molecular masses and molar masses of molecular substances, and between formula masses and molar masses of ionic compounds. In other words,... 

The chemical formula of a compound provides the relative number of atoms (or moles) of each element in a compound and can therefore be used to determine numerical relationships between moles of the compound and moles of its constituent elements. This relationship can be extended to mass by using the molar masses of the compound and its constituent elements. 

Quantitative Calculations When needed, the relationship between the analyte and the analytical signal is given by the stoichiometry of any relevant reactions. Calculations are simplified, however, by applying the principle of conservation of mass. The most frequently encountered example of a direct volatilization gravimetric analysis is the determination of a compound s elemental composition. 

When you analyze data, you may be asked to compare measured quantities. Or, you may be asked to determine the relative amounts of elements in a compound. Suppose, for example, you are asked to compare the molar masses of the diatomic gases, hydrogen (H2) and oxygen (O2). The molar mass of hydrogen gas equals 2.00 g/mol the molar mass of oxygen equals 32.00 g/mol. The relationship between molar masses can be expressed in three ways a ratio, a fraction, or a percent. 

The mass of one mole of atoms of an element—the molar mass, with units of grams per mole—is numerically equal to the dimensionless relative atomic mass of that element, and the same relationship holds between the molar mass of a compound and its relative molecular mass. Thus, the relative molecular mass of water is 18.0152, and its molar mass is 18.0152 g mol . ... 

The molar mass, which expresses the equivalent relationship between 1 mole of a substance and its mass in grams, can be used as a conversion factor. We multiply by the molar mass of an element or compound (Jt, in g/mol) to convert a given amount (in moles) to mass (in grams) ... 

In 1803, John Dalton introduced the first modern atomic theory. He developed the relationship between elements and atoms and established that compounds were combinations of elements. He also introduced the concept of atomic mass. 

The specific radioactivity describes the relationship between radioactivity and mass and is the decay rate (counts per unit of time) per unit mass of an element or compound— the SI unit is Bq kg For practical purposes specific radioactivity also is defined in dpm g or dpm mole Activity concentration (or radioactive concentration) is given in Bq m or Bq For example, the total atoms in 1 g of P (ti/2 = 14.3 day) is ... 

Mass percent composition is one way to understand how much chlorine is in a particular chlorofluorocarbon or, more generally, how much of a constituent element is present in a given mass of any compound. However, we can also approach this type of problem in a different way. Chemical formulas contain within them inherent relationships between atoms (or moles of atoms) and molecules (or moles of molecules). For example, the formula for CCI2F2 teUs us that 1 mol of CCI2F2 contains 2 mol of Cl atoms. We write the ratio as ... 

---